Name: Date: =2 =1−4

[Pages:11]Name: _____________________________________________________________ Date: _________________

Algebra 2

Function Operations & Compositions

If f (x) = x2 -1 , g(x) = 2x - 3, and h(x) = 1 - 4x , find the following new functions, as well as any values indicated.

1. a. ( f - g)(x) =

b. ( f - g)(3) =

2. a. (g + f )(x) =

b. (g + f )(-2) =

3. a. ( f + h)(x) =

b. ( f + h)(0) =

4. a. (g h)(x) =

b. (g h)(4) =

5. a. ( f g)(x) =

6.

a.

f g

(x)

=

7.

a.

g h

(x)

=

b. ( f g)(-1) =

b.

f g

(2)

=

b.

g h

(0)

=

Let f(x) = 2x ? 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following:

1. f(g(-3))

2. f(h(7))

3. g(h(24))

4. h(f(9))

5. g(f(0))

6. h(g(-4))

7. f(g(h(2)))

8. h(g(f(5)))

9. g(f(h(-6)))

10. f(f(x))

11. g(g(x))

12. h(h(x))

Composition of Functions, MATH100



Composition of Functions, MATH100

Please work with a partner on this exercise. The purpose of this worksheet is to read and use graphs of functions in the context of composition of functions. Definition: The graph of a function h(x) is the set of points (x, h(x)).

Shown above are sketches of the graphs of two functions, f(x) (left) and g(x) (right). Use the graphs to answer the questions below. The first question has been done for you.

1. Find f(g(-1)). To find f(g(-1)), we first find g(-1) then use the graph of f(x) to find f(g(-1)). First find find the point in the right hand graph that is on the x-axis at x = -1. The graph of g(x) lies above the x-axis at this point, so trace up from the x-axis to the point (-1,3) on the graph. The definition of the graph of a function tells us that this point on the graph has coordinates (-1, g(-1)), so it must be true that g(-1) = 3. Now find f(g(-1)) = f(3). In the left side graph of f(x), locate the point on the x-axis where x = 3. Trace up from this point to the point (3,4) on the graph of f(x). Use the definition of the graph of f(x) to conclude that f(3) = 4. f(g(-1)) = f(3) = 4.

2. Find f(g(0)). g(0) =

f(g(0)) = 3. Find g(f(0)).

4. Find f(g(-1)).

5. Bonus: Use the graphs to find the zeros of the function g(f(x)).

1 of 1

5/12/2016 8:02 PM

Algebra 2

Compositions of Functions

Perform the indicated operation.

1) g(x) = 3x + 3 Find (g g)(6)

3) g(n) = n - 2 h(n) = n2 + 3 Find (g h)(-8)

5) g(n) = 2n - 5 Find (g g)(6)

7) h(x) = 4x + 4 Find (h h)(-4)

9) f (n) = 2n - 2 g(n) = 2n - 4 Find ( f g)(-9)

11) h(n) = 4n - 1 g(n) = 4n - 4 Find (h g)(2n)

13) g(n) = n - 3 h(n) = n - 1 Find (g h)(4n)

15) g(n) = 3n + 4 h(n) = 2n + 2 Find (g h)(-n)

17) g(a) = -4a + 3 h(a) = 2a + 3 Find (g h)(a + 4)

19) g(x) = 4x - 4 f (x) = -x - 2 Find (g f )(-2x)

ID: 1

Name___________________________________

Date________________ Period____

2) g(x) = x2 - 2 + x h(x) = 4x + 1 Find (g h)(-3)

4) g(x) = 3x + 2 Find (g g)(7)

6) f (a) = 4a - 2 Find ( f f )(4)

8) g(x) = 2x - 2 f (x) = x2 + 5x Find (g f )(1)

10) g(x) = x - 4 f (x) = -3x2 + 2 Find (g f )(1)

12) h(x) = 2x + 5 Find (h h)(3 - y)

14) f (a) = 4a - 2 g(a) = 3a - 2 Find ( f g)(1 + a)

16) f (t) = 2t - 1 g(t) = -3t2 - 4 Find ( f g)(-2 + t)

18) g(n) = -2n + 2 f (n) = n3 - n Find (g f )(n - 2)

20) h(x) = 4x - 5 g(x) = x2 - 2x Find (h g)(4z)

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Worksheet by Kuta Software LLC

1) 66 5) 9

9) -46 13) 4n - 4

17) -8a - 41 20) 64z2 - 32z - 5

Answers to Compositions of Functions (ID: 1)

2) 108

3) 65

6) 54

7) -44

10) -5

11) 32n - 17

14) 12a + 2

15) -6n + 10

18) -2n3 + 12n2 - 22n + 14

19) 8x - 12

4) 71

8) 10

12) -4 y + 27 16) -6t2 + 24t - 33

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Worksheet by Kuta Software LLC

Name:________________________________ Date:________________ Period:______

COMPOSITE FUNCTION WORKSHEET Directions: Show all work for credit. Work must be neat and answer must be circled.

For 1- 9: Let f(x) = 2x ? 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following:

1. f(g(-3))

2. f(h(7))

3. (gh)(24)

4. f(g(h(2)))

5. h(g(f(5)))

6. g(f(h(-6)))

7. f( x + 1)

8. g(3a)

9. h( x ? 2)

For 10-11: Let f(x) = -3x + 7 and g(x) = 2x2 ? 8. Compute the following:

10. f(g(x))

11. (gf)(x)

If f (x) 3x 5 and g(x) x2 ,

12. find f g3

If f (x) 9x 9 and g(x) x 9,

13. find f g10

If f (x) 4x 2 and g(x) x 8,

14. find f g12

If f (x) 3x 4 and g(x) x2 ,

15. find g f 2

If f (x) 2x 1 and g(x) x2 5,

16. find g f 2

Given f (x) 9x 3 and g(x) x4 ,

17. find f gx

Given f (x) 2x 5 and g(x) x 2,

18. find f gx

Given f (x) x2 7 and g(x) x 3,

19. find f gx

Given f (x) 4x 3 and g(x) x2 ,

20. find g f x

Given f (x) x 1 and g(x) x2 2x 8,

21. find g f x

Kuta Software - Infinite Algebra 2

Function Inverses

State if the given functions are inverses.

1)

g(x) = 4 -

3 x

2

f (x) = 1 x + 3

2 2

3) f (n) = -16 + n

4

g(n) = 4n + 16

5) f (n) = -(n + 1)3 g(n) = 3 + n3

7) f (x) = 4 + 2

-x - 2

h(x) = - 1

x + 3

Find the inverse of each function.

9)

h(x) =

3

x

- 3

Name___________________________________ Date________________ Period____

2) g(n) = -12 - 2n

3

f (n) = -5 + 6n

5

4) f (x) = - 4 x - 16

7 7

g(x) = 3 x - 3

2 2

6) f (n) = 2(n - 2)3

3

g(n) = 4 + 4n

2

8) g(x) = - 2 - 1

x

f (x) = - 2

x + 1

10) g(x) = 1 - 2

x

11) h(x) = 2x3 + 3

12) g(x) = -4x + 1

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Worksheet by Kuta Software LLC

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